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# 8 identical machines, working alone and at their constant rates, take

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Math Expert
Joined: 02 Sep 2009
Posts: 46319
8 identical machines, working alone and at their constant rates, take [#permalink]

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23 Aug 2015, 22:50
00:00

Difficulty:

15% (low)

Question Stats:

75% (00:44) correct 25% (00:47) wrong based on 256 sessions

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8 identical machines, working alone and at their constant rates, take 6 hours to complete a job lot. How long would it take for 3 such machines to perform the same job?

A. 2.25 hours
B. 8.75 hours
C. 12 hours
D. 14.25 hours
E. 16 hours

Kudos for a correct solution.

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Senior Manager
Joined: 21 Jan 2015
Posts: 287
Location: India
Concentration: Strategy, Marketing
GMAT 1: 620 Q48 V28
WE: Sales (Consumer Products)
8 identical machines, working alone and at their constant rates, take [#permalink]

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23 Aug 2015, 23:08
2
1
Bunuel wrote:
8 identical machines, working alone and at their constant rates, take 6 hours to complete a job lot. How long would it take for 3 such machines to perform the same job?

A. 2.25 hours
B. 8.75 hours
C. 12 hours
D. 14.25 hours
E. 16 hours

Ans: E

Solution: 8 machines take 6 hrs to complete the job, so one machine will take 8*6= 48 hrs to complete the job alone.
three machine together will finish the work in = 48/3 = 16 hrs.
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Manager
Joined: 14 Mar 2014
Posts: 148
GMAT 1: 710 Q50 V34
Re: 8 identical machines, working alone and at their constant rates, take [#permalink]

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24 Aug 2015, 01:16
2
Bunuel wrote:
8 identical machines, working alone and at their constant rates, take 6 hours to complete a job lot. How long would it take for 3 such machines to perform the same job?

A. 2.25 hours
B. 8.75 hours
C. 12 hours
D. 14.25 hours
E. 16 hours

Kudos for a correct solution.

IMO: E

Let each machine do 1 unit of work for 1 hour
8 machines --> 8 units of work in 1 hour
For 6 hours = 8*6 = 48 Units of total work is done.

Now this 48 Units of total work must be done by 3 machines
3 units of work(3 machines) ---> 1 hour
for 48 Units of work
3*16 ---> 1*16 hours

Thus a total of 16 hours
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Manager
Joined: 07 Apr 2015
Posts: 177
Re: 8 identical machines, working alone and at their constant rates, take [#permalink]

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24 Aug 2015, 02:10
1
8 machines take 6 hours for 1 job. Therefore their rate is 1/6. Divide by number of machines 8, and then multiply by 3 to get the rate for 3 machines.

=> $$1/6 * 1/8 = 1/48$$
=> $$1/48 * 3 = 3/48$$

Take the reciprocal for the time taken, 48/3 = 16 Hours
Manager
Joined: 10 Jun 2015
Posts: 121
Re: 8 identical machines, working alone and at their constant rates, take [#permalink]

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24 Aug 2015, 02:43
1
1
Bunuel wrote:
8 identical machines, working alone and at their constant rates, take 6 hours to complete a job lot. How long would it take for 3 such machines to perform the same job?

A. 2.25 hours
B. 8.75 hours
C. 12 hours
D. 14.25 hours
E. 16 hours

Kudos for a correct solution.

As number of machines reduced it will take more time to complete the same job.
we have to increase the number of hours.
multiply 6 hours with the increasing ratio, that is, 8/3
You get 16 hours.
Intern
Joined: 20 Jul 2014
Posts: 3
Schools: IIMB'17
8 identical machines, working alone and at their constant rates, take [#permalink]

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25 Aug 2015, 14:42
1
1
By using formula
M1D1H1/w1=M2D2H2/w2 we can deduce
8*6 =3*H2
Therefore H2=16
E
Senior Manager
Joined: 15 Sep 2011
Posts: 345
Location: United States
WE: Corporate Finance (Manufacturing)
8 identical machines, working alone and at their constant rates, take [#permalink]

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25 Aug 2015, 17:33
1
Bunuel wrote:
8 identical machines, working alone and at their constant rates, take 6 hours to complete a job lot. How long would it take for 3 such machines to perform the same job?

A. 2.25 hours
B. 8.75 hours
C. 12 hours
D. 14.25 hours
E. 16 hours

Kudos for a correct solution.

A, B and C are out automatically since the number of machines are less than half, and less than half results in more than double the time. Between D and E, option E, for 16 hours is the same amount of hours (48) as the whole 8 needed. Option E.

Kr,
Mejia
Director
Joined: 21 May 2013
Posts: 649
Re: 8 identical machines, working alone and at their constant rates, take [#permalink]

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27 Aug 2015, 08:14
1
Bunuel wrote:
8 identical machines, working alone and at their constant rates, take 6 hours to complete a job lot. How long would it take for 3 such machines to perform the same job?

A. 2.25 hours
B. 8.75 hours
C. 12 hours
D. 14.25 hours
E. 16 hours

Kudos for a correct solution.

Using chain rule, (8 machines*6 hours)/1 job done=(3 machines*no of hours)/1 job done
No of hours=16 hours
Math Expert
Joined: 02 Sep 2009
Posts: 46319
Re: 8 identical machines, working alone and at their constant rates, take [#permalink]

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30 Aug 2015, 08:45
Bunuel wrote:
8 identical machines, working alone and at their constant rates, take 6 hours to complete a job lot. How long would it take for 3 such machines to perform the same job?

A. 2.25 hours
B. 8.75 hours
C. 12 hours
D. 14.25 hours
E. 16 hours

Kudos for a correct solution.

VERITAS PREP OFFICIAL SOLUTION:

Given that 8 machine rates = 1 job / 6 hours, you can divide both sides of that equation by 8 to find the rate of 1 machine working alone. That means that the rate of one machine is 1 job / 48 hours. Because you have 3 machines, you can multiply that rate by 3 to find the rate of 3 machines, which is then 3 jobs / 48 hours which reduces to 1 job / 16 hours. Therefore it will take 16 hours for 3 machines to perform the job.

A helpful shortcut to this problem is to recognize that the time and the number of machines are inversely proportional (fewer machines will take longer). So since you have 3/8 as many machines, it will take 8/3 as long. 8/3 * 6 = 16, answer choice E.
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Posts: 80
Re: 8 identical machines, working alone and at their constant rates, take [#permalink]

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16 Sep 2017, 07:36
Time taken by each machine = 8*1/x = 1/6 . This gives x= 48 hours.
Time taken by 3 machines = 48/3 = 16 hours (E)
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Re: 8 identical machines, working alone and at their constant rates, take [#permalink]

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21 Sep 2017, 14:59
Bunuel wrote:
8 identical machines, working alone and at their constant rates, take 6 hours to complete a job lot. How long would it take for 3 such machines to perform the same job?

A. 2.25 hours
B. 8.75 hours
C. 12 hours
D. 14.25 hours
E. 16 hours

The rate for 8 machines is 1/6. Let’s use the following proportion to determine the rate (which we can call n) of 3 machines:

8/(1/6) = 3/n

48 = 3/n

48n = 3

n = 3/48 = 1/16

We see that the rate of 3 machines is 1/16; thus, it will take 3 machines 16 hours to perform the same job.

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Manager
Joined: 22 Nov 2016
Posts: 236
Location: United States
GPA: 3.4
8 identical machines, working alone and at their constant rates, take [#permalink]

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08 Nov 2017, 22:37
8 machines perform 1 job in 6 hours
1 machine performs $$\frac{1}{8}$$ th of the job in 6 hours
1 machine performs $$\frac{1}{(8*6)}$$ job in 1 hour

Hence rate of 1 machine is $$\frac{1}{48}$$
Rate of 3 machines is $$3*\frac{1}{48}$$ = $$\frac{1}{16}$$

or, 3 machines will finish 1 job in 16 hours.
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8 identical machines, working alone and at their constant rates, take   [#permalink] 08 Nov 2017, 22:37
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